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1.
We study the fractional decomposition of the quantum enveloping affine algebras
and
with vanishing central charge in the limit
. This decomposition is based on the bosonic representation and can be related to fractional supersymmetry and k-fermionic spin. The quantum affine algebras and the classical ones are equivalent in the fermionic realization. 相似文献
2.
The CPT Group of the Dirac Field 总被引:2,自引:2,他引:0
Miguel Socolovsky 《International Journal of Theoretical Physics》2004,43(9):1941-1967
Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields
,
and
, where
and
. These sets are given by
,
,
and
,
,
. Then
, and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively,
and
, which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that
and
, where
is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of
by
, isomorphic to a semidirect product of these groups; S6 and S8 are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group
, which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with
, which is then called the matrix CPT group. It turns out that
, where
is the dicyclic group of 8 elements and S10 is the symmetric group of 10 elements. Since
, the quaternion group, and
, the 0-sphere, then
. 相似文献
3.
J. R. Choi 《International Journal of Theoretical Physics》2003,42(4):853-861
We use the dynamical invariant method to derive quantum-mechanical solution of time-dependent Hamiltonian system consisting quadratic potential, inverse quadratic potential, and
. The term in Hamiltonian containing
gives the expression such as
in coordinate space, which we can often meet in radial equation of quantum many body problem. The wave functions differed only a time-dependent phase factor from the eigenstates of the invariant operator Î and expressed in terms of an associated Laguerre function. 相似文献
4.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
5.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
6.
This Letter concerns an extension of the quantum spinor construction of
. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of
. 相似文献
7.
Michael Keyl 《International Journal of Theoretical Physics》1998,37(1):375-385
The major subject of algebraic quantum fieldtheory is the study of nets of local C*-algebras, i.e.,maps
(
) assigning to each open,relatively compact region of space-time (M, g) aC*-algebra
(
), whose self-adjoint elements describe localobservables measurable in the region
. A question discussed recently in a number ofpapers is how much information about the geometricstructure of the underlying space-time (M, g) is encoded in the algebraicstructure of the net
(
). Followingthese ideas, it is demonstrated in this paper howspace-time-related concepts like causality and observerscan be described in a purely algebraic way, i.e., using only thelocal algebras
(
).These results are then used to show how the space-time(M, g) can be reconstructed from the set
loc := {
(
)|
M open,
compact} of local algebras. 相似文献
8.
A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle
of modules of Cartan differential forms over a bounded region X of a curved C
-smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L
+ := SO(1,3), is presented.
is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form
. The mathematical structure employed to model this replacement of
is a principal finitary spacetime sheaf
of quantum causal sets
with structure group G
n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g
n-valued connection 1-form
on it, which is a section of its subsheaf
.
is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature
as some sort of finitary and causal Lorentzian quantum gravity. 相似文献
9.
J. A. Espichan Carrillo A. Jr. Maia 《International Journal of Theoretical Physics》1999,38(8):2185-2196
We study the influence of boundary conditions on energy levels of interacting fields in a box and discuss some consequences when we hange the size of the box. In order to do this we calculate the energy levels of bound states of a scalar massive field nteracting with another scalar field through the Lagrangian
=
> in a one-dimensional box on which we impose Dirichlet boundary conditions. We find that the gap between the bound states changes with the size of the box in a nontrivial way. For the case where the masses of the two fields are equal and for large box the energy levels of Dashen-Hasslacher-Neveu (DHN model) are recovered and we have a kind of boson condensate for the ground state. Below a critical box size
the ground-state level splits, which we interpret as particle-antiparticle production under small perturbations of box size. Below other critical sizes,
and
, of the box, the ground state and firstexcited state merge in the continuum part of the spectrum. 相似文献
10.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
11.
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang–Baxter equation). In this paper we use the quantum affine reflection algebras of type
to determine new n-parameter families of nondiagonal reflection matrices. These matrices describe the reflection of vector solitons off the boundary in
affine Toda field theory. They can also be used to construct new integrable vertex models and quantum spin chains with open boundary conditions. 相似文献
12.
Stefano De Leo Zbigniew Oziewicz Waldyr A. Rodrigues Jayme Vaz 《International Journal of Theoretical Physics》1999,38(9):2349-2369
We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford
-algebra
. A fundamental ingredient in ourmultivectorial algebraic formulation is a
-complex geometry,
. We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on
, where denotes an
-algebra of functions. 相似文献
13.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
14.
V. Gaftoi J. Lopez-Bonilla G. Ovando 《International Journal of Theoretical Physics》1999,38(3):939-943
Weert found a superpotential
for the bounded part of the Maxwelltensor
associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator
for the superpotential
. 相似文献
15.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
16.
Juri Agresti Roberto De Pietri Luca Lusanna Luca Martucci 《General Relativity and Gravitation》2004,36(5):1055-1134
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy
, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO)
. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without
introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in
. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's
, which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation. 相似文献
17.
We construct embeddings of boundary algebras
into ZF algebras
. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for
and without for
), this connection allows to make the link between different approaches of the systems with boundaries. The construction uses the well-bred vertex operators built recently, and is classified by reflection matrices. It relies only on the existence of an R-matrix obeying a unitarity condition, and as such can be applied to any infinite dimensional quantum group. 相似文献
18.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
19.
We show that the inclusion of a term C
abcd
C
abcd
in the action can remove the recently described anisotropic singularity occurring on the hypersurface F () = 0 of scalar-tensor theories of gravity of the type
preserving, by construction, all of their isotropic solutions. We show that, in principle, a higher order term of this type can arise from considerations about the renormalizability of the semiclassical approach to the theory. Such result brings again into consideration the quintessential models recently proposed based in a conformally coupled scalar field
with potential
, that have been discharged as unrealistic precisely by their anisotropic instabilities on the hypersurface F () = 0. 相似文献
20.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献